Standard parallel MRI techniques accelerate imaging acquisition by exploiting sensitivity variation in array coils to unfold aliased images [1] or replace phase encoding steps [2] in the reconstruction of equi-spacedly subsampled MRI data. In multi-slice MRI, the number of available slices is usually limited by scan time, data acquisition window or specific absorption rate (SAR). The goal of this work is to develop a super slice interpolation (SSI) method for multi-slice MRI by exploiting sensitivity variation along the slice direction to reconstruct thinner slice images from a set of thick images acquired with multiple receiver coils.

Figure 1 illustrates the concept of proposed SSI method. SSI generates multiple thinner slices from each acquired thick slice using coil sensitivity maps acquired with thinner slices. Let dl(i,j) denote a pixel in a thick slice of the l-th coil at location (i,j), the encoding equation of parallel multi-slice MRI can be formulated as: $$$d_{l}\left(i,j\right)=\sum_k^Ks_{l}\left(i,j,k\right)m\left(i,j,k\right),l=1,2,...,L$$$ (1)

where m(i,j,k), k = 1, 2, …, K, denotes pixels in thin slices which contribute to signal dl(i,j) and K is the number of the target pixels, sl(i,j,k) denotes sensitivity of the l-th coil at location (i,j,k) and L is the number of coils. For brevity, the above encoding equation can be expressed in a vector form:

$$$d=Em$$$ (2)

where E denotes the sensitivity encoding matrix constructed form sensitivity maps. The goal of SSI is to reconstruct m by inversing Eq. (2).

Because lower intra-voxel sensitivity variation along the slice direction leads to severely ill-conditioned encoding matrix, the direct inversion of Eq. (2) will result in large noise amplification. To suppress noise amplification, Tikhonov regularization is introduced to reconstruction[3], which can be formulated as:

$$$\widehat{m}=argmin_m\left\{\mid\mid Em-d\mid\mid_2^2+\lambda\mid\mid m\mid\mid_2^2\right\}$$$ (3)

where $$$\mid\mid \Box \mid\mid_2^2$$$ denote the square of L2 norm, and λ is the regularization parameter which controls the noise suppression effect but at the expense of spatial resolution along the slice direction. In this work, λ was experientially determined as 0.2 by a visual inspection for the tradeoff between signal-to-noise ratio (SNR) and slice separation accuracy.

The performance of proposed SSI method was evaluated on multi-slice fast spin echo data acquired on a Philips Achieva 3T MRI scanner. Phantom data were acquired with a sixteen-channel abdomen coil, and in vivo head data were acquired with an eight-channel human head coil. The scan parameters were: TE/TR = 80/3000 ms, FOV = 230×230 mm2, matrix size = 230×230, slice gap = 0 mm, echo train length = 16. Thirty-two slices with 6 mm thickness were acquired as thick slices, and sixty-four slices with 3 mm thickness were acquired as thin slices for performance evaluation. Sensitivity maps were calculated as the multi-coil thin slice images divided by their root-sum-of-square combination.

Figure 2 and 3 separately show phantom imaging results from two typical acquired 6 mm slice image. From regions pointed by solid arrows, it can be observed that the SSI-generated 3 mm slice images contained structures close to those in the directly acquired 3 mm slice images. Figure 4 shows in vivo head imaging results from one typical 6 mm slice image. The structures and margins were blurred in the acquired 6 mm thickness images. In contrast, the SSI-separated images exhibited more clearly defined margins, as pointed by arrows, which were similar to those in directly acquired 3 mm thickness images. It can also be observed that the cerebellum in the SSI results were successfully separated into two parts, which were similar to corresponding contents in directly acquired 3 mm thickness images.The proposed SSI method provides a novel way to exploit sensitivity variation along the slice direction to decrease slice thickness in multi-slice MRI. SSI is a totally postprocessing method with coil sensitivity, and thus applicable to all multi-slice acquisitions without the need to modify pulse sequences. SSI may help in tackling the high SAR problem of fast spin echo imaging particularly at high field MRI, and increasing the slice resolution of multi-slice echo planer imaging in dynamic MRI.Our results clearly demonstrated the capability of SSI in generating thin slice images from thick slice MRI data. The proposed SSI method can be combined with in-plane parallel MRI methods for further acceleration, and has potential to obtain more slices with decreased thickness in scenarios where acquisition window or SAR limits the available number of slices.